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Effect of a transverse flow on the convective dissolution of $\textbf{CO}_{\textbf{2}}$ in water

Patrice Meunier,Max Riedinger,Adam Walsh,Francois Nadal,Christophe Brouzet

Published 2025 in Journal of Fluid Mechanics

ABSTRACT

Abstract We study experimentally, numerically and theoretically the gravitational instability induced by dissolution of carbon dioxide with a forced lateral flow. The study is restricted to the model case of a vertical Hele-Shaw cell filled with water. While a transverse (horizontal) flow is continuously forced through the whole cell, the carbon dioxide is introduced above the liquid–gas interface so that a $\textrm {CO}_2$ -enriched diffusive layer gradually forms on top of the liquid phase. The diffusive layer destabilises through a convective process which entrains the $\textrm {CO}_2$ –water mixture towards the bottom of the cell. The concentration fields are measured quantitatively by means of a pH-sensitive dye (bromocresol green) that reveals a classic fingering pattern. We observe that the transverse background flow has a stabilising effect on the gravitational instability. At low velocity (i.e. for small thickness-based Péclet numbers), the behaviour of the system is hardly altered by the background flow. Beyond a threshold value of the Péclet number ( $\textit{Pe} \sim 15$ ), the emergence of the fingering instability is delayed (i.e. the growth rate becomes smaller), while the most unstable wavelength is increased. These trends can be explained by the stabilising role of the Taylor–Aris dispersion in the horizontal direction and a model is proposed, based on previous works, which justifies the scalings observed in the limit of large Péclet number for the growth rate ( $\sigma ^\star \sim \textit{Pe}^{-4}$ ) and the most unstable wavelength ( $\lambda ^\star \sim \textit{Pe}^{\,5/2}$ ). The flux (rate mass transfer) of $\textrm {CO}_2$ in the nonlinear regime is also weakly decreased by the background transverse flow.

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